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Question
The value of `(z + 3)(barz + 3)` is equivalent to ______.
Options
|z + 3|2
|z – 3|
z2 + 3
None of these
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Solution
The value of `(z + 3)(barz + 3)` is equivalent to |z + 3|2 .
Explanation:
Given that: `(z + 3)(barz + 3)`
Let z = x + yi
So `(z + 3)(barz + 3)` = (x + yi + 3)(x – yi + 3)
= [(x + 3) + yi][(x + 3) – yi]
= (x + 3)2 – y2 i2
= (x + 3)2 + y2
= |x + 3 + iy|2
= |z + 3|2
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